A charge q moving with a velocity through a magnetic field of induction experiences a magnetic force perpendicular both to and . Experimental observations show that the magnitude of the force is proportional to the magnitude of , the speed of the particle, the charge q and the sine of the angle θ between and . That is, the magnetic force, Fm = qv B sin θ
∴
Therefore, at every instant acts in a direction perpendicular to the plane of and .
If the moving charge is negative, the direction of the force acting on it is opposite to that given by the right-handed screw rule for the cross-product × .
If the charged particle moves through a region of space where both electric and magnetic fields are present, both fields exert forces on the particle.
The force due to the electric field is .
The total force on a moving charge in electric and magnetic fields is called the Lorentz force :
Special cases :
(i) is parallel or antiparallel to : In this case, Fm = qvB sin 0° = 0. That is, the magnetic force on the charge is zero.
(ii) The charge is stationary {v = 0) : In this case, even if q ≠ 0 and B ≠ 0, Fm = q(0)B sin θ = 0. That is, the magnetic force on a stationary charge is zero.